Laws of Spatially Structured Population Dynamics on a Lattice
We consider spatial population dynamics on a lattice, following a type of a contact (birth–death) stochastic process. We show that simple mathematical approximations for the density of cells can be obtained in a variety of scenarios. In the case of a homogeneous cell population, we derive the cellul...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-07-01
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| Series: | Physics |
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| Online Access: | https://www.mdpi.com/2624-8174/4/3/52 |
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| author | Natalia L. Komarova Ignacio A. Rodriguez-Brenes Dominik Wodarz |
| author_facet | Natalia L. Komarova Ignacio A. Rodriguez-Brenes Dominik Wodarz |
| author_sort | Natalia L. Komarova |
| collection | DOAJ |
| description | We consider spatial population dynamics on a lattice, following a type of a contact (birth–death) stochastic process. We show that simple mathematical approximations for the density of cells can be obtained in a variety of scenarios. In the case of a homogeneous cell population, we derive the cellular density for a two-dimensional (2D) spatial lattice with an arbitrary number of neighbors, including the von Neumann, Moore, and hexagonal lattice. We then turn our attention to evolutionary dynamics, where mutant cells of different properties can be generated. For disadvantageous mutants, we derive an approximation for the equilibrium density representing the selection–mutation balance. For neutral and advantageous mutants, we show that simple scaling (power) laws for the numbers of mutants in expanding populations hold in 2D and 3D, under both flat (planar) and range population expansion. These models have relevance for studies in ecology and evolutionary biology, as well as biomedical applications including the dynamics of drug-resistant mutants in cancer and bacterial biofilms. |
| first_indexed | 2024-03-09T22:48:39Z |
| format | Article |
| id | doaj.art-b081ea07f8854006a1282b1b3cfa3344 |
| institution | Directory Open Access Journal |
| issn | 2624-8174 |
| language | English |
| last_indexed | 2024-03-09T22:48:39Z |
| publishDate | 2022-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Physics |
| spelling | doaj.art-b081ea07f8854006a1282b1b3cfa33442023-11-23T18:25:31ZengMDPI AGPhysics2624-81742022-07-014381283210.3390/physics4030052Laws of Spatially Structured Population Dynamics on a LatticeNatalia L. Komarova0Ignacio A. Rodriguez-Brenes1Dominik Wodarz2Department of Mathematics, University of California Irvine, Irvine, CA 92617, USADepartment of Mathematics, University of California Irvine, Irvine, CA 92617, USADepartment of Mathematics, University of California Irvine, Irvine, CA 92617, USAWe consider spatial population dynamics on a lattice, following a type of a contact (birth–death) stochastic process. We show that simple mathematical approximations for the density of cells can be obtained in a variety of scenarios. In the case of a homogeneous cell population, we derive the cellular density for a two-dimensional (2D) spatial lattice with an arbitrary number of neighbors, including the von Neumann, Moore, and hexagonal lattice. We then turn our attention to evolutionary dynamics, where mutant cells of different properties can be generated. For disadvantageous mutants, we derive an approximation for the equilibrium density representing the selection–mutation balance. For neutral and advantageous mutants, we show that simple scaling (power) laws for the numbers of mutants in expanding populations hold in 2D and 3D, under both flat (planar) and range population expansion. These models have relevance for studies in ecology and evolutionary biology, as well as biomedical applications including the dynamics of drug-resistant mutants in cancer and bacterial biofilms.https://www.mdpi.com/2624-8174/4/3/52evolutionary dynamicsmutationsagent-based modelingsomatic evolutioncomputational methodsmathematical modeling |
| spellingShingle | Natalia L. Komarova Ignacio A. Rodriguez-Brenes Dominik Wodarz Laws of Spatially Structured Population Dynamics on a Lattice Physics evolutionary dynamics mutations agent-based modeling somatic evolution computational methods mathematical modeling |
| title | Laws of Spatially Structured Population Dynamics on a Lattice |
| title_full | Laws of Spatially Structured Population Dynamics on a Lattice |
| title_fullStr | Laws of Spatially Structured Population Dynamics on a Lattice |
| title_full_unstemmed | Laws of Spatially Structured Population Dynamics on a Lattice |
| title_short | Laws of Spatially Structured Population Dynamics on a Lattice |
| title_sort | laws of spatially structured population dynamics on a lattice |
| topic | evolutionary dynamics mutations agent-based modeling somatic evolution computational methods mathematical modeling |
| url | https://www.mdpi.com/2624-8174/4/3/52 |
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